Competitive Adsorptive Mechanism of H2/N2 in LTA/FAU Zeolites by Molecular Simulations and Experiments

For industrial tail gas to be converted into high-purity hydrogen, the H2-N2 mixture needs to be separated efficiently. This work examined the adsorption characteristics and competitive mechanisms of H2 and N2 on LTA- and FAU-type zeolites, at 77 K, 298 K, and 0.1–10 bar by thoroughly analyzing results of adsorption capacity experiments and molecular simulations. In the Grand Canonical Monte Carlo (GCMC) simulations, the force field causing a molecular dipole of H2 and the polarization force field of N2 are first applied. The accuracy of the force field was experimentally verified. The findings indicate that N2 and H2 loading on Ca-FAU (Ca-LTA) are higher than Na-FAU (Na-LTA). On NaX at 77 K, the highest adsorption selectivity (N2/H2) is observed; on NaA at 298 K, it is the opposite. The GCMC data findings demonstrate that H2 and N2 have remarkably similar adsorption sites, with framework oxygen atoms and non-framework cations serving as the main adsorption sites for adsorbate molecules. Furthermore, the rate at which H2 diffuses is higher than that of N2. The study of redistribution charge before and after adsorption demonstrated that N2 has a greater affinity for the framework oxygen atoms than H2. This study provides a molecular theoretical foundation for the adsorption behavior of H2-N2 mixture in zeolites.


Introduction
H 2 is a green and clean energy source with advantages of cleanliness, no pollution, zero emissions, and wide applications.The heat of the combustion of hydrogen is higher than that of most fuels based on the same mass, making it an ideal substitute for fossil fuels.According to sources, hydrogen can be divided into gray hydrogen [1][2][3], blue hydrogen [4,5], green hydrogen [6], and hydrogen-rich tail gas [7,8].Currently, over 95% of hydrogen generation occurs through steam methane reforming (SMR), resulting in what is commonly referred to as "gray hydrogen", or via coal gasification, which produces "brown hydrogen".A promising approach toward decarbonized hydrogen involves combining SMR or gasification with carbon capture and sequestration (CCS), resulting in "blue hydrogen".If renewable or nuclear power is used to supply the electricity for this process, the resulting hydrogen would be decarbonized and recognized as "green hydrogen" [9].While gray hydrogen production currently accounts for a high proportion, it does result in significant pollution due to the discharge of harmful gasses.Furthermore, although environmentally friendly, green hydrogen can be costly, and its application rate is currently limited.However, the recovery of hydrogen-rich tail gas offers significant benefits for the comprehensive utilization of hydrogen and carbon neutrality.Currently, there is significant interest in the industrial exhaust effect caused by processes such as steam methane reforming (H 2 /N 2 /CO 2 ) [10,11], ammonia production (H 2 /N 2 /NH 3 ) [12], and coke oven gas (H 2 /N 2 /CH 4 ) [13].These processes result in the production of a substantial amount of H 2 -N 2 mixture.As a result, many researchers have focused on binary or ternary mixtures containing richer impurities such as CO 2 /CH 4 [14].According to Carbajo's study on the adsorption and separation behavior of gas mixtures such as H 2 /N 2 /CO 2 /CH 4 /CO in zeolites, H 2 or N 2 had a lesser interaction with zeolite framework atoms [15].This made it harder to separate them from other gasses compared to those gasses with higher polarizability.The associated physical properties of N 2 and H 2 gasses are shown in Table 1.Yaremov et al. investigated the effects of microporous zeolites' pore parameters and surface characteristics (at 77, 197, and 253 K; 760 torr) on the adsorption of H 2 , N 2 , CO, and CH 4 .According to this study, the adsorption inertia of H 2 helped in gas separation from other gasses [16].There is research on the separation of H 2 -N 2 mixture predominantly using MOFs [17], activated carbons [18][19][20], membranes [21,22], and zeolites [23].A zeolite is a kind of porous material widely used in industry.It can selectively adsorb molecules based on their size, shape, and polarity.Li et al. studied N 2 adsorption in Linde Type A (LTA) and truncated octahedron (FAU)-type zeolites at 1 bar and 300 K [24,25].The results indicated that N 2 had superior adsorption performance in FAU-type zeolites, with an adsorption capacity of up to 16.26 mol/kg.Then, the N 2 adsorption capacity of the LiX zeolite was twice that of the Type A zeolite with extra-framework cations of Ca (CaA) zeolite [26].The results highlighted the benefits of FAU-and LTA-type zeolites for adsorptive H 2 or N 2 .However, the study of the competitive adsorption mechanism of H 2 -N 2 mixture in FAU-and LTA-type zeolites is not clear.Most researchers have utilized molecular simulation techniques employing classical force fields to investigate the adsorption of H 2 or N 2 in zeolites.In general, simulations employing classical force fields fail to replicate experimental findings.To address the inaccuracy of classical force fields, we examined the accuracy of hydrogen force field parameters, specifically dipole moments, and incorporated polarization correction in the nitrogen force field parameters.The simulation results for single-component adsorption isotherms exhibit strong agreement with experimental test results, confirming the credibility of the force field parameters and the models.This paper analyzes the effects of cation type (Na + and Ca 2+ ), adsorption temperature (77 K and 298 K), and pressure (0-10 bar) on the adsorption capacity of H 2 and N 2 in LTA-and FAU-type zeolites using the force field parameters.In addition, it examines the competitive diffusion behavior of adsorbate molecules and investigates the law of competitive diffusion.Furthermore, the competitive adsorption mechanism of H 2 and N 2 in zeolites is examined in terms of the adsorption sites and the charge density.

Adsorption Isotherm
The adsorption isotherms of H 2 and N 2 on LTA-and FAU-type zeolites were measured at 77 K (0.1-1 bar) and 298 K (0.1-10 bar).We conducted experimental H 2 and N 2 adsorption isotherms in the zeolite at 298 K, and the H 2 isotherms at 77 K were obtained from the works of Kotoh [27], Du [28], Langmi [29], and Kazansky [30], while the N 2 isotherm at 77 K was obtained from Sircar [31].First, the one-component computed isotherms of H 2 and N 2 were compared with the available experimental data.It was observed that the simulated isotherms using the previously developed force field do not fit the experimental data shown in Figures 1 and 2, and Evagelia used Feynman-Hibbs to explain the H 2 quantum effect involving dispersion-type interactions in their force field [32].However, all the adsorption isotherms from this study's force field, as shown in Figures 1 and 2, exhibit reasonable agreement between experiments and simulations, and using experience, the values of relative average deviation (RAD) lower than 30% are acceptable, as shown in Table S1.The simulated isotherms of H 2 and N 2 at 77 K slightly over-predict the adsorption isotherms for NaX.Nevertheless, the simulated isotherms of H 2 and N 2 at 298 K slightly under-predict the adsorption isotherms below 60 kPa for NaA.By fitting the adsorption isotherms results with Langmuir model, the Langmuir model parameters for H 2 and N 2 were estimated, and they are presented in Table S2.The adsorption isotherms depicted in Figures 1 and 2 conform to the Langmuir isotherm, indicating that the adsorption of H 2 and N 2 on the LTAand FAU-type zeolites follows a microporous adsorption behavior.In the 0-1 bar range at 77 K, the N 2 loading on the LTA-and FAU-type zeolites is approximately twice the value of H 2 loading, as shown in Figure 1a,b.However, in the 0-10 bar range at 298 K, the N 2 loading on the LTA-and FAU-type zeolites exceeds ten times the H 2 loading values shown in Figure 2a,b.It is observed that the adsorption value of H 2 is greater in the FAU zeolite than in the LTA-type zeolite at 298 K. Furthermore, for FAU-and LTA-type zeolites at 77 K, the H 2 and N 2 adsorption capacities of Ca-FAU (Ca-LTA) are greater than those in Na-FAU (Na-LTA).In most cases, the adsorption affinity of H 2 in Ca-FAU (Ca-LTA) is stronger than that of Na-FAU (Na-LTA), which can be attributed to the smaller radius of Na + and the shorter interaction distance with adsorbent molecules.When Na + is exchanged with Ca 2+ in the zeolite, the non-framework cation decreases, therefore expanding the pore volume of the zeolite framework and allowing for an increase in the space available for H 2 adsorption.
fit the experimental data shown in Figures 1 and 2, and Evagelia used Feynman-Hibbs to explain the H2 quantum effect involving dispersion-type interactions in their force field [32].However, all the adsorption isotherms from this study s force field, as shown in Figures 1 and 2, exhibit reasonable agreement between experiments and simulations, and using experience, the values of relative average deviation (RAD) lower than 30% are acceptable, as shown in Table S1.The simulated isotherms of H2 and N2 at 77 K slightly over-predict the adsorption isotherms for NaX.Nevertheless, the simulated isotherms of H2 and N2 at 298 K slightly under-predict the adsorption isotherms below 60 kPa for NaA.By fitting the adsorption isotherms results with Langmuir model, the Langmuir model parameters for H2 and N2 were estimated, and they are presented in Table S2.The adsorption isotherms depicted in Figures 1 and 2 conform to the Langmuir isotherm, indicating that the adsorption of H2 and N2 on the LTA-and FAU-type zeolites follows a microporous adsorption behavior.In the 0-1 bar range at 77 K, the N2 loading on the LTAand FAU-type zeolites is approximately twice the value of H2 loading, as shown in Figure 1a,b.However, in the 0-10 bar range at 298 K, the N2 loading on the LTA-and FAU-type zeolites exceeds ten times the H2 loading values shown in Figure 2a-b.It is observed that the adsorption value of H2 is greater in the FAU zeolite than in the LTA-type zeolite at 298 K. Furthermore, for FAU-and LTA-type zeolites at 77 K, the H2 and N2 adsorption capacities of Ca-FAU (Ca-LTA) are greater than those in Na-FAU (Na-LTA).In most cases, the adsorption affinity of H2 in Ca-FAU (Ca-LTA) is stronger than that of Na-FAU (Na-LTA), which can be attributed to the smaller radius of Na + and the shorter interaction distance with adsorbent molecules.When Na + is exchanged with Ca 2+ in the zeolite, the non-framework cation decreases, therefore expanding the pore volume of the zeolite framework and allowing for an increase in the space available for H2 adsorption.fit the experimental data shown in Figures 1 and 2, and Evagelia used Feynman-Hibbs to explain the H2 quantum effect involving dispersion-type interactions in their force field [32].However, all the adsorption isotherms from this study s force field, as shown in Figures 1 and 2, exhibit reasonable agreement between experiments and simulations, and using experience, the values of relative average deviation (RAD) lower than 30% are acceptable, as shown in Table S1.The simulated isotherms of H2 and N2 at 77 K slightly over-predict the adsorption isotherms for NaX.Nevertheless, the simulated isotherms of H2 and N2 at 298 K slightly under-predict the adsorption isotherms below 60 kPa for NaA.By fitting the adsorption isotherms results with Langmuir model, the Langmuir model parameters for H2 and N2 were estimated, and they are presented in Table S2.The adsorption isotherms depicted in Figures 1 and 2 conform to the Langmuir isotherm, indicating that the adsorption of H2 and N2 on the LTA-and FAU-type zeolites follows a microporous adsorption behavior.In the 0-1 bar range at 77 K, the N2 loading on the LTAand FAU-type zeolites is approximately twice the value of H2 loading, as shown in Figure 1a,b.However, in the 0-10 bar range at 298 K, the N2 loading on the LTA-and FAU-type zeolites exceeds ten times the H2 loading values shown in Figure 2a-b.It is observed that the adsorption value of H2 is greater in the FAU zeolite than in the LTA-type zeolite at 298 K. Furthermore, for FAU-and LTA-type zeolites at 77 K, the H2 and N2 adsorption capacities of Ca-FAU (Ca-LTA) are greater than those in Na-FAU (Na-LTA).In most cases, the adsorption affinity of H2 in Ca-FAU (Ca-LTA) is stronger than that of Na-FAU (Na-LTA), which can be attributed to the smaller radius of Na + and the shorter interaction distance with adsorbent molecules.When Na + is exchanged with Ca 2+ in the zeolite, the non-framework cation decreases, therefore expanding the pore volume of the zeolite framework and allowing for an increase in the space available for H2 adsorption.

Adsorption Selectivity and Heat
Adsorption selectivity is a vital indicator used to evaluate the adsorption performance of adsorbent materials.In order to explore the H 2 and N 2 adsorption properties in LTA-and FAU-type zeolites, we apply the ideal adsorption solution theory (IAST) to predict the selectivity of H 2 -N 2 mixture.The selectivity is calculated using Equation (1): where q 1 and q 2 are the adsorption capacities, and p 1 and p 2 are the partial pressures.
In this study, the selectivity of N 2 /H 2 was predicted at 77 K within the range of 0-1 bar, and at 298 K within the range of 0-10 bar.Using the same molar fractions of H 2 and N 2 , we can easily investigate the competitive adsorption behavior of the H 2 -N 2 mixture.All calculations were performed using the PyIAST package (3.12.4) [33].As shown in Figure 3, the selectivity of N 2 /H 2 in the FAU-type zeolite is higher than that in the LTA-type zeolite at 77 K. Additionally, the selectivity of N 2 /H 2 in Ca-FAU (Ca-LTA) is lower than that in Na-FAU (Na-LTA) at 298 K.The greatest selectivity of N 2 /H 2 is observed in NaX at 77 K, while the greatest selectivity of N 2 /H 2 is observed in NaA at 298 K.The adsorption selectivity from the binary N 2 -H 2 mixture via GCMC simulations is shown in Figure S1.The results indicate that the selectivity values obtained from binary mixture GCMC simulation are consistent with those predicted using the IAST.
Adsorption selectivity is a vital indicator used to evaluate the adsorp performance of adsorbent materials.In order to explore the H2 and N2 adsorp properties in LTA-and FAU-type zeolites, we apply the ideal adsorption solution th (IAST) to predict the selectivity of H2-N2 mixture.The selectivity is calculated u Equation ( 1): where q1 and q2 are the adsorption capacities, and p1 and p2 are the partial pressures.
In this study, the selectivity of N2/H2 was predicted at 77 K within the range o bar, and at 298 K within the range of 0-10 bar.Using the same molar fractions of H2 N2, we can easily investigate the competitive adsorption behavior of the H2-N2 mixt All calculations were performed using the PyIAST package (3.12.4) [33].As show Figure 3, the selectivity of N2/H2 in the FAU-type zeolite is higher than that in the L type zeolite at 77 K. Additionally, the selectivity of N2/H2 in Ca-FAU (Ca-LTA) is lo than that in Na-FAU (Na-LTA) at 298 K.The greatest selectivity of N2/H2 is observe NaX at 77 K, while the greatest selectivity of N2/H2 is observed in NaA at 298 K. adsorption selectivity from the binary N2-H2 mixture via GCMC simulations is show Figure S1.The results indicate that the selectivity values obtained from binary mix GCMC simulation are consistent with those predicted using the IAST.In Figure 4, we present contributions from different interactions to the energ adsorption of H2 and N2 in FAU-and LTA-type zeolites at high loadings though calculations.It is evident that the primary contribution to the energy of adsorption fo and N2 is the significant host-guest interaction, which consists of a dispersive and electrostatic component.The main difference is that N2 exhibits higher electros interaction energies compared to H2, while they have similar dispersive contribution the simulations of the FAU-and LTA-type zeolites, the calculated energy of adsorptio primarily influenced by the adsorption site binding energy, with only a m contribution from the guest-guest interaction.However, the guest-guest interactio approximately zero since we used a one-site guest model.To investigate the effec temperature on adsorption, we conducted the calculation using single-component equilibrium adsorption isotherms at 77 K and 298 K, according to the Virial Method The heat of adsorption at infinite dilution is provided in Table 2.In Figure 4, we present contributions from different interactions to the energy of adsorption of H 2 and N 2 in FAU-and LTA-type zeolites at high loadings though MC calculations.It is evident that the primary contribution to the energy of adsorption for H 2 and N 2 is the significant host-guest interaction, which consists of a dispersive and an electrostatic component.The main difference is that N 2 exhibits higher electrostatic interaction energies compared to H 2 , while they have similar dispersive contributions.In the simulations of the FAU-and LTA-type zeolites, the calculated energy of adsorption is primarily influenced by the adsorption site binding energy, with only a minor contribution from the guest-guest interaction.However, the guest-guest interaction is approximately zero since we used a one-site guest model.To investigate the effect of temperature on adsorption, we conducted the calculation using single-component gas equilibrium adsorption isotherms at 77 K and 298 K, according to the Virial Method [34].The heat of adsorption at infinite dilution is provided in Table 2

Adsorption Sites
To investigate the H2 and N2 adsorption mechanism on the zeolites employed, we performed MC simulations in an NVT ensemble (with one H2 or N2 molecule per unit cell) under 1 bar at 77 K and 298 K. Figure 5 shows the interaction between H2 (N2) and the LTA-type zeolite at 77 K, and Figure 6 shows the interaction between H2 (N2) and the FAUtype zeolite at 77 K.The optimized geometry reveals a minimal ONaA-H distance of 0.97 Å and the minimal ONaA-N distance of 0.6736 Å.In Figure 6, we can observe the interaction of H2 (N2) with the FAU-type zeolite.The optimized geometry reveals a minimal OCaX-N distance of 0.37 Å and a minimal ONaX-N distance of 0.21 Å.In the preferred sites, the behavior of H2 is similar to that of N2.With similar adsorption sites, N2 and zeolites are closer to each other, resulting in better adsorption.The binding interaction between H2 and N2 is observed to be stronger in the FAU-type zeolite compared to the LTA-type zeolite.This observation holds true at 298 K as well, as shown in Figures S2 and S3.The adsorption site is consistent with the adsorption density pattern (Figures S4-S7).From the adsorption density figures, it is evident that H2 exhibits stronger adsorption density at 77 K in the vicinity of oxygen atoms in the zeolite.The adsorbate molecules interact more strongly with zeolites, and as the temperature increases, the H2 molecules disperse to binding sites with lower binding energies, resulting in weaker interactions with the zeolite.On the other hand, N2 adsorption behaves in the opposite manner, exhibiting stronger adsorption densities with the zeolite at 298 K. Significant density changes were observed in the CaA and NaX zeolites.

Adsorption Sites
To investigate the H 2 and N 2 adsorption mechanism on the zeolites employed, we performed MC simulations in an NVT ensemble (with one H 2 or N 2 molecule per unit cell) under 1 bar at 77 K and 298 K. Figure 5 shows the interaction between H 2 (N 2 ) and the LTA-type zeolite at 77 K, and Figure 6 shows the interaction between H 2 (N 2 ) and the FAUtype zeolite at 77 K.The optimized geometry reveals a minimal O NaA -H distance of 0.97 Å and the minimal O NaA -N distance of 0.6736 Å.In Figure 6, we can observe the interaction of H 2 (N 2 ) with the FAU-type zeolite.The optimized geometry reveals a minimal O CaX -N distance of 0.37 Å and a minimal O NaX -N distance of 0.21 Å.In the preferred sites, the behavior of H 2 is similar to that of N 2 .With similar adsorption sites, N 2 and zeolites are closer to each other, resulting in better adsorption.The binding interaction between H 2 and N 2 is observed to be stronger in the FAU-type zeolite compared to the LTA-type zeolite.This observation holds true at 298 K as well, as shown in Figures S2 and S3.The adsorption site is consistent with the adsorption density pattern (Figures S4-S7).From the adsorption density figures, it is evident that H 2 exhibits stronger adsorption density at 77 K in the vicinity of oxygen atoms in the zeolite.The adsorbate molecules interact more strongly with zeolites, and as the temperature increases, the H 2 molecules disperse to binding sites with lower binding energies, resulting in weaker interactions with the zeolite.On the other hand, N 2 adsorption behaves in the opposite manner, exhibiting stronger adsorption densities with the zeolite at 298 K. Significant density changes were observed in the CaA and NaX zeolites.To investigate the interaction of H 2 and N 2 with zeolite atoms, we employed AIMD to examine the behavior of the H 2 -N 2 mixture (H 2 /N 2 , 50/50, v/v) within the zeolite under the NVT ensemble.The radial distribution function (RDF) was obtained by calculating the molecular trajectories of H 2 and N 2 .Figures 7 and 8 present the zonal and average densities of H 2 and N 2 based on O, Si, Al, and non-framework cations in LTA-and FAU-type zeolites at 1 bar and 77 K.The shape and intensity of the peaks provide evidence of the interaction sites and adsorption capacities of H 2 and N 2 on the zeolites.It is evident that the zeolite exhibits a stronger interaction preference for N 2 , as indicated by the local of the primary peak.In Figure 7, the initial peak occurs at 0.75 Å, indicating the highest likelihood of H 2 being present at 0.75 Å.Similarly, in Figure 8, the radial distribution function of N 2 displays the highest peak at 0.5 Å, indicating the highest probability of N 2 being present at 0.5 Å.These findings clearly show that the main peaks representing the interactions between N 2 and zeolites are higher than those of H 2 .The intensity of the main peak for H 2 is 6, while that for N 2 is 8, which aligns with the observation in Figure 4 regarding the larger adsorption energy for the interaction of N 2 and zeolites.The initial peaks observed in Figures 7 and 8, respectively, correspond to the oxygen atoms of framework.This suggests that the oxygen atoms of the framework assume the closest positions to the unrestricted movement of H 2 and N 2 .Consequently, this finding supports the notion that the interaction energy between the H 2 (N 2 ) and the oxygen atoms of the framework accounts for a significant portion of the adsorption energy between the host and guest.The same principle applies at 298 K; please refer to Figures S8 and S9 for supporting evidence.To investigate the interaction of H2 and N2 with zeolite atoms, we employed AIMD to examine the behavior of the H2-N2 mixture (H2/N2, 50/50, v/v) within the zeolite under the NVT ensemble.The radial distribution function (RDF) was obtained by calculating the molecular trajectories of H2 and N2.Figures 7 and 8 present the zonal and average densities of H2 and N2 based on O, Si, Al, and non-framework cations in LTA-and FAUtype zeolites at 1 bar and 77 K.The shape and intensity of the peaks provide evidence of the interaction sites and adsorption capacities of H2 and N2 on the zeolites.It is evident that the zeolite exhibits a stronger interaction preference for N2, as indicated by the local of the primary peak.In Figure 7, the initial peak occurs at 0.75 Å, indicating the highest likelihood of H2 being present at 0.75 Å.Similarly, in Figure 8, the radial distribution function of N2 displays the highest peak at 0.5 Å, indicating the highest probability of N2 being present at 0.5 Å.These findings clearly show that the main peaks representing the interactions between N2 and zeolites are higher than those of H2.The intensity of the main peak for H2 is 6, while that for N2 is 8, which aligns with the observation in Figure 4 regarding the larger adsorption energy for the interaction of N2 and zeolites.The initial peaks observed in Figures 7 and 8, respectively, correspond to the oxygen atoms of framework.This suggests that the oxygen atoms of the framework assume the closest positions to the unrestricted movement of H2 and N2.Consequently, this finding supports the notion that the interaction energy between the H2 (N2) and the oxygen atoms of the framework accounts for a significant portion of the adsorption energy between the host and guest.The same principle applies at 298 K; please refer to Figures S8 and S9 for supporting evidence.Because the dynamic diameters of H2 and N2 are similar to the effective pore diameter of the LTA-and FAU-type zeolites, diffusion plays a key role in the absorption and separation processes of H2 or N2.The diffusion of the adsorbate molecules in the zeolite is influenced not only by their dynamic diameter but also by their interaction with the oxygen atoms of the framework.
We analyzed the dynamic behavior of a H2-N2 mixture (H2/N2, 50/50, v/v) in FAUand LTA-type zeolites at different temperatures by calculating the mean square displacements (MSDs) and the self-diffusion coefficients.Figures 9 and 10 depict the relationship between the adsorbate molecular motion and equilibrium time.It is observed that the diffusion of H2 is greater in FAU-type zeolite than in LTA-type zeolite at 298 K. Additionally, for both FAU-and LTA-type zeolites at 298 K, the H2 and N2 diffusion capacities of Ca-FAU (Ca-LTA) are greater than those of Na-FAU (Na-LTA).During the free movement of adsorbate molecules, H2 diffuses more easily than N2 in the pores of LTA-and FAU-type zeolites.Karger conducted a diffusion study on H2 in NaX and NaA zeolites and found that the type of zeolite influences the diffusion process of H2, with the diffusion rate decreasing as the size of the zeolite pores decreases [35,36] where the average is taken over time t for the mean square displacement of the center of mass position vectors r of all the molecules N in the system; and ‹› indicates the overall average.Because the dynamic diameters of H 2 and N 2 are similar to the effective pore diameter of the LTA-and FAU-type zeolites, diffusion plays a key role in the absorption and separation processes of H 2 or N 2 .The diffusion of the adsorbate molecules in the zeolite is influenced not only by their dynamic diameter but also by their interaction with the oxygen atoms of the framework.
We analyzed the dynamic behavior of a H 2 -N 2 mixture (H 2 /N 2 , 50/50, v/v) in FAUand LTA-type zeolites at different temperatures by calculating the mean square displacements (MSDs) and the self-diffusion coefficients.Figures 9 and 10 depict the relationship between the adsorbate molecular motion and equilibrium time.It is observed that the diffusion of H 2 is greater in FAU-type zeolite than in LTA-type zeolite at 298 K. Additionally, for both FAU-and LTA-type zeolites at 298 K, the H 2 and N 2 diffusion capacities of Ca-FAU (Ca-LTA) are greater than those of Na-FAU (Na-LTA).During the free movement of adsorbate molecules, H 2 diffuses more easily than N 2 in the pores of LTA-and FAU-type zeolites.Karger conducted a diffusion study on H 2 in NaX and NaA zeolites and found that the type of zeolite influences the diffusion process of H 2 , with the diffusion rate decreasing as the size of the zeolite pores decreases [35,36].The linear nature of the MSD indicates the reliability of the simulation process.The self-diffusion coefficients of H 2 and N 2 are calculated using the Einstein relation, as shown in Equation (2): where the average is taken over time t for the mean square displacement of the center of mass position vectors r of all the molecules N in the system; and ‹› indicates the overall average.
The calculated results are shown in Tables 3 and 4.Among the four types of zeolites NaX zeolites exhibit the highest self-diffusion coefficients for H2 and N2 at 77 K, with a ratio of 7.6 (H2/N2).Similarly, CaX zeolites show the largest self-diffusion coefficients for H2 and N2 at 298 K, with a ratio of 6.54 (H2/N2).The self-diffusion coefficients of H2 and N in Na-FAU (Na-LTA) are lower than those in Ca-FAU (Ca-LTA).The calculated results are shown in Tables 3 and 4.Among the four types of zeolites, NaX zeolites exhibit the highest self-diffusion coefficients for H2 and N2 at 77 K, with a ratio of 7.6 (H2/N2).Similarly, CaX zeolites show the largest self-diffusion coefficients for H2 and N2 at 298 K, with a ratio of 6.54 (H2/N2).The self-diffusion coefficients of H2 and N2 in Na-FAU (Na-LTA) are lower than those in Ca-FAU (Ca-LTA).The calculated results are shown in Tables 3 and 4.Among the four types of zeolites, NaX zeolites exhibit the highest self-diffusion coefficients for H 2 and N 2 at 77 K, with a ratio of 7.6 (H 2 /N 2 ).Similarly, CaX zeolites show the largest self-diffusion coefficients for H 2 and N 2 at 298 K, with a ratio of 6.54 (H 2 /N 2 ).The self-diffusion coefficients of H 2 and N 2 in Na-FAU (Na-LTA) are lower than those in Ca-FAU (Ca-LTA).

Investigation of Charge Density
To investigate the effect of H 2 and N 2 on the chemical environment within the zeolite pores during adsorption at the atomic level, DFT calculations were performed to explore the redistribution of charge density in this system after adsorbing H 2 or N 2 molecules.The charge density analysis of LTA-and FAU-type zeolites is shown in Figures S10 and S11.It is clear from the figures that before the adsorption of gases, the electron cloud is concentrated around the zeolite pores.After the adsorbate molecules are adsorbed onto the zeolites, the electron density is transferred to the adsorbate molecules.The adsorption properties of the adsorbate molecules within the framework are determined using the oxygen atoms of the framework and the non-framework cations.As shown in Figure S10, due to the strong electron withdrawing ability of the zeolite atoms, the electrons of the H atoms in H 2 molecules migrate to the framework atoms, especially the oxygen atoms.Similarly, in Figure S11, the N atoms in N 2 donate some charges, leading to the interactions with the zeolite atoms.In comparing Figures 11 and 12, it can be observed that the charge density transfers between oxygen atoms, and N 2 is more pronounced, which is likely due to the denser electron cloud distribution of N 2 molecules.The adsorbate molecules show an increased charge density on one side of the oxygen atoms of the zeolite framework and a decreased charge density on the other side in Figures 11 and 12. H 2 and N 2 exhibit a blue area near the side of the oxygen atoms of the framework, indicating a decrease in charge density, while the framework atoms show a red area, indicating an increase in charge density.The electrostatic potentials of N 2 and H 2 in Ca-FAU (Ca-LTA) demonstrate larger values than those in Na-FAU (Na-LTA).A comparison of the analyses in Figures 11 and 12 reveals that the charge transfer in the pores of LTA-and FAU-type zeolites after the adsorption of N 2 is more pronounced than that of H 2 and that N 2 is more affected by the chemical environment in the zeolite pores.

Framework and Adsorbate: Models and Force Fields
The zeolite flexible framework has little impact on the simulation of small-molecule adsorption.In this study, the rigid structure model was employed for simulation [26].The atoms were considered "frozen", neglecting interatomic interactions between framework atoms to significantly shorten the simulation time [37].The zeolite structures used in this study were taken from crystallographic files (CIFs) of the IZA database, with additional framework cations inserted for structural optimization [38].The geometric structure was optimized using Density Functional Theory (DFT).The overall unit cell maintains a rigid structure.We analyzed the geometric structure with the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation functional, associated with the third-generation dispersion correction (DFT-D3) to avoid weak interaction, implemented in the CP2K package (8.2.0) [39][40][41].The density cut-off was set to 500 Ry, and the overall energy converged to within 10 −6 eV.The physicochemistry characteristics of the investigated LTA and FAU samples in this study are shown in Table 5.The accuracy of the force field is essential for GCMC simulations.In order to validate the accuracy of our GCMC simulations, we compared the specific force field parameters of Vujić [42], General [43], Evagelia [32], Kowsari [44,45], Pantatosaki [46], and Huang [47].The force field previously described by J. Marcos takes into consideration the influence of the dipole moment of the H 2 molecule and the polarization of the electric field generated by the local structure of the zeolite.For hydrogen, we used a one-site point charge model, while for N 2 , we used the parameters reported by Xuan [48].There are strong Coulomb interactions between adsorbates and non-framework cations as well as mobility of these cations.So, the location and density of the non-framework cations influence the adsorption behavior of H 2 and N 2 in zeolite structures [49].The cation Ca 2+ parameters reported by Du and the cation Na + parameters reported by Farida were employed to describe interactions in this work [45,50].The force field parameters and partial charges are presented in Table 6.The simulation accuracy of classical force fields is not sufficient when the polarization effect of N 2 is neglected.To enhance the simulation accuracy, the polarization force field is introduced by scaling the Lennard-Jones (L-J) interaction between N 2 and zeolite atoms with a parameter λ ∈ [0, 1] [51,52].The atomic polarizabilities used in this study were from the literature using Equation (3).For this study, λ was set to 0.4 by fitting the experimental data to the simulation results.
where λ is a scaling factor between 0 and 1 used for rescaling the Lennard-Jones energy parameters; α i means the polarizability of atom i ; α max means the max polarizability; and ε i means the initial force field parameter.λ = 1 means that N 2 has the same interaction potential energy function with other molecules, and λ = 0 means that N 2 does not interact with other molecules.

Simulation Details
The separation of H 2 and N 2 adsorption in LTA-and FAU-type zeolites was performed using the RASPA code [53,54].The cut-off radius was set to half the length of the cell edge in the simulation box, without considering tail corrections, and by applying periodic boundary conditions to maintain a three-dimensional spatial structure.Only cations and adsorbate molecules were allowed to move, while the zeolite structure remained rigid.In these simulations, the following trial moves were used for the cations: translation (50%) and random (50%).For the H 2 and N 2 molecules, the trial moves were carried out: translation (20%), rotation (20%), insertion (20%), and random (40%).The total number of cations remained constant during the simulations, and only translation movements and regrow were considered for this type of particle.Based on the reported crystallographic locations of Na + , Na + molecules were expected to enter the sodality cages in FAU-type zeolites, but not in LTA-type zeolites [55].Therefore, blocking spheres were exclusively used for LTA-type zeolites in our investigation, with the ionic radius of Na + (r Na + = 1.16) serving as the probe size.The simulations were performed for 5 × 10 5 cycles, with 25,000 initialization cycles and 20,000 equilibration cycles.The final simulation result was obtained by averaging the results of the two simulation processes.The excess adsorption data were used for investigation [56].The excess adsorption capacity (n exc ) was obtained by relating the absolute adsorption capacity (n abs ) to the pore volume of the adsorbent (V g ) and the molar density of the native gas phase (ρ g ), using Equation (4): In the He-void (ϕHe) calculations, the particle method with the Rosenbluth algorithm was used [57].The largest cavity diameter (LCD), pore volume, and accessible surface area (ASA) were determined using Zeo ++ software packages (0.3) [58].The interaction between the adsorbates and the zeolite atoms was calculated based on electrostatic and van der Waals force interactions.The electrostatic interactions were computed using the Coulomb force, while the interatomic interaction parameters were determined using Lorentz-Berthelot mixing rules [59]; Equation (5) was used for this calculation: where σ ij and ε ij are the L-J potential parameters.Van der Waals interactions were described using the 12-6 Lennard-Jones (L-J), and the Ewald method was employed to calculate long-range electrostatic interactions with a relative accuracy of 10 −6 [60]; Equation (6) was used for this calculation: where r ij is the interatomic distance between the i and j atoms.
MD simulation was performed using the RASPA code.Molecular dynamic runs of H 2 -N 2 (H 2 /N 2 , 50/50, v/v) molecules were conducted in a 25 × 25 × 25 Å box at 77 and 298 K, with periodic boundary conditions imposed in all directions.The MD simulation was run for 1 ns with a time step of 0.5 fs in the NVT ensemble.The simulations included 2 × 10 6 cycles, with 2000 initialization cycles and 20,000 equilibration cycles.
To explore the distribution of H 2 and N 2 molecules in zeolites, the ab initio molecular dynamic (AIMD) simulation was employed using the CP2K program (8.2.0).The simulations employed the Gaussian plane wave method, implemented in the Quickstep module [61], with the input file using the Multiwfn code [62].The simulation was performed in the NVT ensemble using the BASIS_MOLOPT basis set [63] and GTH_POTENTIALS pseudopotential [64].The employed density functional was the PBE with the DFT-D3 dispersion corrections.The CSVR thermostat with a temperature relaxation time of 0.5 ps was used to keep the temperature at 298 K during the simulations [65].All reported properties were averaged over at least 500 ps, and the time step was set to 0.5 fs.

Conclusions
This study investigated the adsorption of H 2 and N 2 single components in Na + /Ca 2+ ion-exchanged LTA-and FAU-type zeolites using GCMC and MD simulations.The adsorption isotherms obtained by the simulations correspond well with the experimental results.It is observed that the Ca 2+ zeolites display a higher H 2 and N 2 adsorption capacity.The IAST predicts the adsorption selectivity of H 2 -N 2 mixture in LTA-and FAU-type zeolites.The findings indicate that the selectivity of N 2 /H 2 is greater for NaX at 77 K and NaA at 298 K. Additionally, the kinetic simulation of H 2 -N 2 mixture diffusion demonstrated that H 2 exhibits the fastest diffusion rate in NaX.This study on adsorption sites for H 2 and N 2 on LTA-and FAU-type zeolites shows that major adsorption sites are located near framework oxygen atoms and non-framework cations.For the non-framework cations, Na + /Ca 2+ , the findings regarding adsorption energy and radial distribution function suggest that the Ca 2+ zeolites exhibit a stronger interaction energy with H 2 and N 2 .Moreover, there is an apparent interaction between the zeolite and N 2 from the redistribution of charge density.This results in a relatively large charge transfer, leading to a stronger adsorption capacity.
. The linear nature of the MSD indicates the reliability of the simulation process.The self-diffusion coefficients of H2 and N2 are calculated using the Einstein relation, as shown in Equation (  −    |  〉     (2)

Figure 12 .
Figure 12.A slice of the redistribution of charge density in (a) NaA, (b) NaX, (c) CaA, and (d) CaX after adsorbing N 2 molecules.

Table 1 .
The physical parameters of H 2 and N 2 . .

Table 2 .
Heats of adsorption at infinite dilution of H 2 and N 2 on zeolites.

Table 5 .
Physicochemistry characteristics of LTA and FAU Systems.

Table 6 .
Lennard-Jones interactions and partial charges.